Radical Unit Mid chapter PARTNER Review

A radical is an expression that includes a root, such as a square root (√) or cube root (∛). It represents the inverse operation of exponentiation.

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs (for square roots) or groups (for cube roots) to simplify.

The conjugate of a binomial expression is formed by changing the sign of the second term. For example, the conjugate of $$a + b$$ is $$a - b$$ .

The conjugate of $$8 - \sqrt{7}$$ is $$8 + \sqrt{7}$$ .

To multiply two radical expressions, multiply the numbers outside the radicals and the numbers inside the radicals separately, then simplify if possible.

The product of $$\sqrt{a} \cdot \sqrt{b}$$ is $$\sqrt{a \cdot b}$$ .

To add or subtract radical expressions, combine like terms. This means you can only add or subtract radicals with the same index and radicand.

The simplified form of $$2\sqrt{24}$$ is $$4\sqrt{6}$$ .

The index of a radical indicates the degree of the root. For example, in $$\sqrt[3]{x}$$ , the index is 3, indicating a cube root.

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, and 16 are perfect squares.